Just for clarity on all my responses in these threads, I'm a (minor) contributor to Nix the Tricks and a personal friend and research partner of the author. An

Just for clarity on all my responses in these threads, I'm a (minor) contributor to Nix the Tricks and a personal friend and research partner of the author. And the one shown right on the front page (for me) cross multiply is how you divide by fractions. a/b / c/d = a/b x d/c. Exactly! And that's exactly what the book recommends. Remember, the target audience of the book is teachers. If a teacher tells them to just draw a butterfly and multiply the matching parts, the students are not actually learning the mathematics. You can use whatever method you want once you understand the mechanics.